Nonrelativistic variational calculations of the positronium molecule and the positronium hydride

Abstract

Highly accurate ground-state nonrelativistic variational calculations of ${\mathrm{Ps}}_{2}$, $^{1}\mathrm{H}\mathrm{Ps}$, and $^{\ensuremath{\infty}}\mathrm{H}\mathrm{Ps}$ are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of the energies obtained are of the order of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for ${\mathrm{Ps}}_{2}$ and $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for HP. Several expectation values have also been computed for each system, as well as electron-positron annihilation rates.